A comparison of multiple linear regression and quantile regression for modeling the internal bond of medium density fiberboard

Multiple linear regression (MLR) and quantile regression (QR) models were developed for the internal bond (IB) of medium density fiberboard (MDF). The data set that aligned the IB of MDF came from 184 independent variables that corresponded to online sensors. MLR models were developed for MDF product types that were distinguished by thickness in inches, i.e., 0.750-inch, 0.6875-inch, 0.625-inch, and 0.500-inch. A best model criterion was used with all possible subsets. QR models were developed for each product type for the most common independent variable of the MLR models for comparison. The adjusted coefficient of determination (R-a(2)) of the MLR models ranged from 72 percent with 53 degrees of freedom to 81 percent with 42 degrees of freedom. The Root Mean Square Errors (RMSE) ranged from 6.05 pounds per square inch (psi) to 6.23 psi; the maximum Variance Inflation Factor (VIF) was 5.6, and all residual patterns were homogeneous. A common independent variable for the 0.750-inch and 0.625-inch MLR models was "Refiner Resin Scavenger %." QR models for 0.750 inch and 0.625 inch indicate similar slopes for the median and average, with different slopes at the fifth and 95th percentiles. "Face Humidity" was a common independent variable for the 0.6875-inch and 0.500-inch MLR models. QR models for 0.6875-inch and 0.500-inch indicate different slopes for the median and average, and instability in IB in the outer fifth and 95th percentiles. The use of QR models to investigate the percentiles of the IB of MDF suggests significant opportunities for manufacturers for continuous improvement and cost savings.